Posting due to the edit.
I'd recommend getting essential books as a core, that would fit any/most scenarios anyway. I'm from the UK so don't know if any of these would be relevant. But just in the hope of helping;
Obviously there are many survival books for different situations.
https://www.amazon.co.uk/dp/B00O6WUOHC/ref=cm_sw_r_cp_apa_glt_PVTGVFSKR9V4S1WDNN3P
I have a toddler son, so prepping with him in mind. I'd highly recommend getting some form of first aid book that includes children and infants. And see if there are any local first aid training courses that you could take. We had one that taught CPR/Heimlich for infants/toddlers etc. Always good to know regardless.
E.g https://www.amazon.co.uk/dp/0241446309/ref=cm_sw_r_cp_awdb_imm_M44Y2Z1TX3V3E2S9S6SB
Another may be a local natural medicine/forager books. And see if there are any allotments near you that teach basic horticulture. Mainly if you don't have long-term food options and the scenario extends longer the 2 weeks.
And home remedy for kids is also handy if only for a short SHTF scenario
https://www.amazon.co.uk/dp/1592336736/ref=cm_sw_r_cp_apa_glt_fabc_RRG5BTS2XYEC4S2D4MWH
I hope these suggestions help in someway, but obviously as their mother, you have the best understanding of what your kids may require.
Don't forget To stock plenty of plain paper and crayons, some board games or books if their inclined to reading. Because two weeks with no Electric, and bored kids, will be a job of its own ๐